Reciprocating compressor simulator and a computer system using the same

ABSTRACT

A method comprising operating a compressor; obtaining operating parameters of the compressor; starting a counter for a crankshaft angle from 0 to 360 degrees; calculating piston displacement and a volume of gas in a cylinder of the compressor as a function of the angle; and calculating a pressure within the cylinder.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority, pursuant to 35 U.S.C. §119(e), of U.S.Provisional Application Ser. No. 60/944,286 entitled “REMOTE MONITORINGSYSTEMS AND METHODS,” filed on Jun. 15, 2007 in the name of James Kongand is hereby incorporated by reference.

BACKGROUND

U.S. Patent Application Publication 2008/0129507 discloses a method foremploying radio frequency (RF) identifier (ID) transponder tags (RFIDtags) to create a unique identifier, termed an RFID signature, for usewithin a data processing system with respect to a person or an object.An interrogation signal is transmitted toward a person or an object withwhich a set of one or more RFID tags are physically associated. A firstset of RFID tag identifiers are obtained from an interrogation responsesignal or signals returned from the set of one or more RFID tags. Amathematical operation is performed on the first set of RFID tagidentifiers to generate an RFID signature value, which is employed as anidentifier for the person or the object within the data processingsystem with respect to a transaction that is performed by the dataprocessing system on behalf of the person or the object. U.S. PatentApplication Publication 2008/0129507 is herein incorporated by referencein its entirety.

U.S. Patent Application Publication 2008/0016353 discloses a method andsystem for verifying the authenticity and integrity of files transmittedthrough a computer network. Authentication information is encoded in thefilename of the file. In a preferred embodiment, authenticationinformation is provided by computing a hash value of the file, computinga digital signature of the hash value using a private key, and encodingthe digital signature in the filename of the file at a predeterminedposition or using delimiters, to create a signed filename. Uponreception of a file, the encoded digital signature is extracted from thesigned filename. Then, the encoded hash value of the file is recoveredusing a public key and extracted digital signature, and compared withthe hash value computed on the file. If the decoded and computed hashvalues are identical, the received file is processed as authentic. U.S.Patent Application Publication 2008/0016353 is herein incorporated byreference in its entirety.

SUMMARY

In one embodiment, the invention provides a method comprising operatingequipment comprising a piston within a cylinder; obtaining parameters ofthe equipment from a data repository; calculating a P-V cycle as afunction of a crankshaft rotation angle; calculating a rod load usingthe P-V cycle values

In another embodiment, the invention provides a method comprisingoperating a compressor; obtaining operating parameters of thecompressor; starting a counter for a crankshaft angle from 0 to 360degrees; calculating piston displacement and a volume of gas in acylinder of the compressor as a function of the angle; and calculating apressure within the cylinder.

Other aspects of the invention will be apparent from the followingdescription and the appended claims.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a schematic diagram of a system in accordance with one ormore embodiments of the invention.

FIG. 2 shows a flowchart of a method in accordance with one or moreembodiments of the invention.

FIG. 3 shows a view of a reciprocating compressor in accordance with oneor more embodiments of the invention.

FIG. 4 shows a Pressure-Volume (P-V) diagram of a compression cycle ofan ideal reciprocating compressor.

FIG. 5 shows an example of a P-V diagram of a compression cycle of areal reciprocating compressor in accordance with one or more embodimentsof the invention.

FIG. 6 shows an example of a P-V diagram of a compression cycle of areal reciprocating compressor, with the effects of the HydroCOMincluded, in accordance with one or more embodiments of the invention.

FIG. 7 shows a table of pressure variables associated with variouscylinder configurations of a compression cycle in a reciprocatingcompressor in accordance with one or more embodiments of the invention.

FIGS. 8A-8B show a flowchart comprising instructions required tocalculate P-V variables as a function of crankshaft angle during onerotation cycle at the head end of the cylinder in a reciprocatingcompressor in accordance with one or more embodiments of the invention.

FIGS. 9A-9B shows a flowchart comprising instructions required tocalculate P-V variables as a function of crankshaft angle during onerotation cycle at the crank end of the cylinder in a reciprocatingcompressor in accordance with one or more embodiments of the invention.

FIG. 10 shows an example of a Rod Load Report in accordance with oneembodiment of the invention.

FIG. 11 shows a computer system in accordance with one or moreembodiments of the invention.

DETAILED DESCRIPTION

Specific embodiments of the invention will now be described in detailwith reference to the accompanying figures. Like elements in the variousfigures are denoted by like reference numerals for consistency.

In the following detailed description of embodiments of the invention,numerous specific details are set forth in order to provide a morethorough understanding of the invention. However, it will be apparent toone of ordinary skill in the art that the invention may be practicedwithout these specific details. In other instances, well-known featureshave not been described in detail to avoid unnecessarily complicatingthe description.

In general, embodiments of the invention provide a system and a methodfor monitoring the working condition of a reciprocating compressor, forexample by monitoring parameters such as inertia, pressure, and totalloads on a piston rod. In one or more embodiments of the invention, eachpiece of equipment has state reporters associated with the equipment.The state reporters may include parameter measuring equipment formeasuring parameters not limited to rotational speed of crankshaft, borediameter, cylinder clearance, one or more individuals viewing theequipment, and other such monitors of the equipment. The state reportersgather unprocessed data that describes the operating parameters of theequipment. The operational parameters may define parameters internal tothe equipment.

The unprocessed data is analyzed at multiple levels of analyses toprovide a complete view of the state of the equipment. Additionally, theunprocessed data may also be pre-stored in a data repository that servesas a reservoir of data used by the levels of analyses, and the statereporter may simply interact with the repository to trigger anappropriate choice of unprocessed data. The levels of analyses mayinclude performance analysis, health analysis, performance analysis, andbenchmark analysis. The levels of analyses create calculated datarepresenting the status of the equipment, the health of the equipment,and the performance of the equipment.

The calculated data may be checked as to whether the data values fallwithin a predefined limit. The limit may be a manufacturer specifiedvalue, based on pre-conducted tests that determine acceptable maximumvalues for the equipment. The limits of data and other manufacturerspecific information about the equipment may be pre-stored in a datarepository. An indicator may indicate the exceeding of the predefinedlimit from the calculated data values and serve as an alarm indicating aconcern about the status of the equipment.

FIG. 1:

FIG. 1 shows a schematic diagram of a system in accordance with one ormore embodiments of the invention. As shown in FIG. 1, the systemincludes a reciprocating compressor equipment (10), a state reportingsub-system (30), a computing sub-system (20), and an indicatorsub-system (40). The system is discussed below.

The reciprocating compressor equipment (10) corresponds to the physicaldevices that is being monitored. For example, the compressor equipment(10) may include crankshafts, piston rods, valves, as well as other suchcomponents.

In one or more embodiments of the invention, the equipment (10) ismonitored by state reporting sub-system (30). Each state reporterincludes functionality to obtain unprocessed data. The state reportermay be a device for conducting measurements, a person monitoring theequipment, or any other monitoring unit that obtains data about theoperating parameters. The state reporter may obtain the equipmentparameters such as density of gas, angular velocity, cylinder clearance,valve coefficient, piston or cylinder bore diameter, specific heat ofgas, mass, mass flow rate, crank shaft rotational speed, as well asother such parameters necessary to perform an analysis of theperformance, and health of equipment.

The computing sub-system (20) corresponds to a sub-system for receivingdata from the state reporter and conducting analysis of received datathat constitute operating parameters of the equipment. The computingsub-system consists of a data repository (26) that may have pre-storeddata about standard operating parameters of the equipment, and the statereporter may interact with the data repository to trigger choice ofappropriate data from the repository. The data repository may alsoinclude data specifying manufacturer-defined operating limits of theequipment, specifications of the equipment, and/or limits above whichhealth and performance of the equipment may be a concern. In one or moreembodiments of the invention, the data repository may be a text filecontaining data or a spreadsheet.

The data repository may have bi-directional data exchange with auser-interface (24). In one or more embodiments of the invention, theuser-interface is a Graphic User Interface (GUI) that plots anend-result or is an application suite for a user to make choices of datastored in the data repository and/or an application suite that acceptsdata from the user for analysis. The user-interface also may have abi-directional data exchange with the Reciprocating Compressor Simulator(22). The Reciprocating Compressor Simulator (RCS) may be an executablecomputer program performing calculations using an input from theinterface based on programmed instructions, and may output data for theGUI to plot. The output data from the RCS may be an indicator ofperformance, and/or health of the equipments. In one or more embodimentsof the invention, the RCS may output a rod load report including theinertia load, pressure load, and total load. In one or more embodimentsof the invention, the RCS may output a text file or spreadsheet into acomputer folder for future analysis.

A reciprocating mass of the compressor equipment is a sum of the massesof the piston, piston rod, piston nut, crosshead, crosshead pin,crosshead nut, and balance mass, which are components of thereciprocating compressor. A rod load report may determine health of thereciprocating compressor equipment. If any of a pressure load, inertiaload, and/or total load exceeds pre-defined limits, an indicatorsub-system (40) may be triggered. In one or more embodiments of theinvention, the indicator sub-system may be a plurality of light-bulbsindicating the state of the equipment with light of different colors,each corresponding to a case when a pre-defined limit is exceeded.Alternately, the indicator sub-system may be an alarm buzzer, an actioninitiating immediate shut-down of the equipment, or an electroniccommunication (e.g., email, text message, etc.) to an individualresponsible for monitoring the equipment. It is obvious to a person ofordinary skill in the art that appropriate processing of the computingoutput may be necessary to trigger the appropriate operation of theindicator sub-system.

In one or more embodiments of the invention, the RCS may includeinstructions for calculating the Pressure-Volume (P-V) cycle a functionof crank shaft rotating angle, with valve losses being accounted for. Inone or more embodiments of the invention, the RCS may calculate thetotal loads on the piston rods of a compressor given the weight of thereciprocating assembly and results of calculations of the P-V cycle. Inone or more embodiments of the invention, the RCS may also calculate thenumber of degrees of rod reversal by checking the total load at eachdegree of crankshaft rotation.

FIG. 2:

FIG. 2 shows the steps involved in an exemplary calculation performed bythe RCS during one rotation cycle of the crankshaft. In Step 201, thereciprocating compressor equipment parameters are obtained from the datarepository or from a user through the GUI. In Step 203, the P-V cycle iscalculated as a function of crankshaft angle, θ, for a complete rotationcycle from 0 to 360 degrees (see e.g., FIGS. 8A, 8B, 9A, 9B below). Step205 involves calculation of the rod loads using the calculated P-Vvalues (discussed below). In Step 207, the rod load values are comparedwith pre-defined limits in the data repository. If the magnitude of thevalues are less than the pre-defined limits, then the calculation forone rotation cycle ends, and is repeated again for the next cycle. Ifthe magnitude of the values are more than the pre-defined limits, thenan alarm may be triggered as discussed above. Further, correctivemeasures may be taken to restore the equipment to a state of properfunctionality by way of a part replacement or change in conditions,where the data repository may also be updated.

FIG. 3:

In one or more embodiments of the invention, a P-V cycle is calculatedas a basis for the theoretical rod load calculations. A typicalreciprocating compressor is shown in FIG. 3 to aid in physicalcorrelation and visualization of variable data calculated by the RCS.

A reciprocating compressor includes a cylinder 320, where compressionmay take place at the head end 375 of the cylinder, the crank end of thecylinder 370, or both, by way of translational movement of the piston310 within the cylinder 320 (only compression corresponding to head end375 is shown in FIG. 3). When compression occurs at both ends, theconfiguration is termed “double acting.” Since the rotation of thecrankshaft 360 contributes to the reciprocal translational movement ofthe piston 310 within the cylinder 320, the compressor is termed“reciprocal.” The crosshead 330 serves as a transition from the pistonrod 315 to the connecting rod 350 of the crankshaft 360. Both the headend 375 and the crank end of the cylinder 370 may each include twovalves: a suction valve 380 and a discharge valve 385 (head end onlylabeled in FIG. 3).

Rotation of crankshaft 360 and the motion of the connecting rod 350cause the crosshead pin 335 to moved back and forth within a bushing.This necessitates reversal of load between tension and compression inthe piston rod 315 at the crosshead pin 335 and the bushing for adequatelubrication of a joint filled with oil. As the crosshead pin 335 movesfrom one side to the other, the oil is squeezed out from the point ofcontact to lubricate the rest of the two surfaces. If this reversal doesnot happen, oil is not applied to a load bearing side of the pin 335 andbushing, and the bearing will eventually fail. In one or moreembodiments of the invention, the RCS may also calculate the number ofdegrees of rod reversal, i.e. load on rod changing from a positive valueto negative value, and vice versa, by checking the total load at eachdegree of crankshaft rotation, which will be discussed later. There mayalso be pre-set positive and negative limits of operation.

FIG. 4:

An ideal compression cycle of a reciprocating compressor is shown inFIG. 4 by way of a P-V diagram, i.e., pressure against cylinder volume.Using the head end compression cycle as an example, the cycle may beexplained starting at point 1 (450). At point 1, the piston is at bottomdead center (BDC) and the cylinder volume is at its maximum. The gas inthe cylinder is at suction pressure P_(s) as shown in FIG. 4, and bothsuction and discharge valves are closed. As the crankshaft rotates andthe piston advances towards the end of the cylinder, the gas trapped inthe cylinder is compressed and the temperature and pressure of the gasrise. As this is an ideal case, there is no friction and no heattransfer, so the change is isentropic.

At point 2 (460), the gas has been compressed enough that the pressurein the cylinder equals the pressure in the discharge line, P_(d). Withan ideal compressor, the discharge valve will open at exactly this pointand there will be no pressure loss across the valve. As the pistoncontinues to the top dead center (TDC) position, the gas in the cylinderis pushed into the discharge line and the pressure in the cylinderremains constant.

When the piston reaches TDC, the cycle is at point 3 (470) on thediagram. The cylinder is now at its minimum volume and the dischargevalve closes. It is to be noted that point 3 is not at 0% cylindervolume, there is some clearance volume between the piston and thecylinder such that the piston does not impact the end of the cylinder.As the crankshaft reverses the direction of piston travel, the gastrapped in this clearance volume expands, and the pressure andtemperature decrease. Again, there are no losses or heat transfer andthis is an isentropic process.

At point 4 (480), the pressure in the cylinder has been reduced down tosuction pressure and the suction valve opens. As the cylinder volumeincreases with piston motion, gas is drawn into the cylinder through thesuction valve. When the piston returns to BDC at point 1, the suctionvalve closes and the cycle is repeated.

In a real compressor, a small amount of differential pressure isrequired to unseat the suction and discharge valves by overcoming thestatic pressure and the valve spring. This means that the pressure inthe cylinder must be higher than the discharge line pressure to open thedischarge valve, and likewise lower than the suction line pressure toopen the suction valve.

Compressor valves affect the performance of reciprocating compressorsdue to the pressure drop caused by gas flow through the valve area, theleakage through the valves in the reverse direction of desired flow, andthe fact that real valves do not close exactly when ideal valves would.The performance parameters directly affected by real compressor valvesare the efficiency, i.e., power and capacity, and the reliability of thecompressor. In one or more embodiments of the invention the RCS takesinto account the effect of real compressor valves on the idealcompression cycle. In one embodiment of the invention, the calculationsare performed by determining a current point on the compression cycle asa function of the crankshaft angle. The crank angle is then increased bya set increment and the calculations are repeated at the new point,using the previous point as a reference.

FIG. 5:

Valve losses appear as pressure drops on the P-V diagram of eachcylinder, and the resulting power loss may be determined due to thepressure drop across the suction and discharge valves in each cylinder.FIG. 5 shows a sample P-V diagram highlighting the difference betweenthe ideal compression cycle and the actual cycle with valve lossesplotted from data calculated by RCS in accordance with one or moreembodiments of the invention.

In one or more embodiments of the invention, a HydroCOM may be acting ona suction valve. A HydroCOM is an unloading device that holds thesuction valve open for part of the compression stroke in a cylinder.This method of a capacity control effectively reduces the volume of gasbeing discharged from the cylinder, as while the HydroCOM is acting onthe suction valve, gas will flow back through this valve instead ofbeing compressed in the cylinder. Once the HydroCOM releases the suctionvalve, the compression process will begin on the volume of gas remainingin the cylinder.

In one or more embodiments of the invention, if a compressor is equippedwith a HydroCOM, its effects may be modeled in the RCS. The HydroCOMposition is taken as a value between 0 and 1, where 1 indicates thatHydroCOM is fully open and not acting on the suction valve, and 0indicates that HydroCOM is acting continuously to hold the suction valveopen throughout the entire compression stroke. When HydroCOM value isbetween 0 and 1, HydroCOM is acting on the suction valve throughout aspecified fraction of the compression stroke.

FIG. 6:

While the HydroCOM acts on the suction valve, gas from the cylinderflows back through the valve and experiences another pressure drop. Thistime the pressure is seen to increase in the P-V diagram as the flowleaves the cylinder instead of entering. There is also a correspondingtemperature rise across the valve. Hence, if the cylinder werecompletely unloaded by the suction valve, the temperature of the gaswould continue to rise and could possibly get hot enough to damage thevalve. Thus, in one or more embodiments of the present invention, theRCS takes into account the valve losses across the suction valve for amore accurate prediction of power in machines using HydroCOMs than byusing a closed-loop solution. FIG. 6 shows a detail of a sample P-Vdiagram of a cylinder equipped with a HydroCOM.

In one or more embodiments of the invention, for every degree ofrotation of crankshaft, an additional condition may be tested todetermine if the HydroCOM is acting. The embodiment of the RCS may be acomputer program code excerpt such as:IF|piston displacement|<stroke*(1−hydrocom position)  (1)THEN HydroCOM actingFIG. 7:

Typically, there are four possible cylinder configurations that may bemodeled by the RCS. If a cylinder is single acting, the compressioncycle is only being performed by one end of the cylinder, either on thehead end (Single Acting Head End or SAHE) or the crank end (SingleActing Crank End or SACE). If both ends of the cylinder are loaded, itis double-acting (DA). This means that the head end and the crank endare both performing compression cycles simultaneously, 180 degreesapart. A cylinder may also be non-acting (NA), which is equivalent toremoving the valves from the cylinder and letting the gas flow throughfreely, i.e., no compression occurs in the cylinder). The examplepressure variables associated with each configuration are shown in FIG.7.

The four most important points to be calculated for each end of thecylinder on the P-V diagram are: (a) Opening of the suction valve, (b)Closing of the suction valve, (c) Opening of the discharge valve, and(d) Closing of the discharge valve.

In one or more embodiments of the invention, the P-V cycle calculationby RCS involves a numerical integration process that begins at 0 degreescrankshaft rotation, which is defined at a minimum head end cylindervolume. At this point, the head end discharge valve has just closed andthe head end is about to start the expansion stroke. Between 0 and 180degrees of crankshaft rotation, the head end undergoes the expansion andsuction stroke while gas in the crank end of the cylinder experiencescompression and discharge. From 180 to 360 degrees of crankshaftrotation, the strokes are reversed. The P-V cycle calculation, i.e. step203 of FIG. 2, is applicable for both the head end and crank endcompression cycle. Although FIG. 3 shows only the head endconfiguration, and the connecting rod associated with the head endcrankshaft, one skilled in the art may easily see that the analysis isvery similar to the head end configuration. The steps involved in theP-V cycle calculation of both head end and crank end configurations willbe described, and the physical phenomena explained with reference toexample calculation variables.

The integration process begins at 0 degrees crankshaft rotation, whichis defined at the minimum head end cylinder volume. FIG. 3 also shows ahead end compressor configuration in a state of 0 degree crankshaftrotation. In order to not limit the calculations to particularconfigurations, the P-V cycle is explained in general using adouble-acting cylinder with one suction valve and one discharge valve atboth the head end and the crank end.

When the compressor is the state of 0 degree crankshaft rotation, thehead end discharge valve has just closed and the head end is about tostart the expansion stroke. Between 0 and 180 degrees of crankshaftrotation, the head end undergoes the expansion and suction stroke, whilegas in the crank end of the cylinder experiences compression anddischarge. From 180 to 360 degrees of crankshaft rotation, the strokesare reversed.

FIGS. 8A, 8B, 9A, and 9B show flowcharts in accordance with one or moreembodiments of the invention. While the various steps in this flowchartare presented and described sequentially, one of ordinary skill willappreciate that some or all of the steps may be executed in differentorders, may be combined or omitted, and some or all of the steps may beexecuted in parallel.

FIGS. 8A & 8B:

Referring to FIGS. 8A and 8B, FIGS. 8A and 8B show the steps involved incalculating the P-V cycle by the RCS for the compression performed inthe head end of the cylinder during one crankshaft rotation cycle, withthe effects of the HydroCOM considered. Those skilled in the art willappreciate that following method may be performed without consideringthe HydroCOM effects, and as such, the invention should not be limitedto considering the HydroCOM effects.

In Step 805 the mechanical parameters such as piston rod diameter,length of piston travel in cylinder, length of connecting rod,crankshaft rotational speed, and other such parameters, and otherpre-stored parameters such as properties of the gas parameters areobtained. In Step 810, a counter for incrementing crankshaft rotationalangle is started from 0 to 360 degrees, where the angle of increment maybe chosen by a user. In one or more embodiments of the invention, thepiston displacement is determined as shown in Step 815. As an example,the piston displacement as a function of angle may be determined fromEquations 2 and 3 as:

$\begin{matrix}{\mspace{79mu}{{{{For}{\mspace{11mu}\;}90{^\circ}} \leq \theta < {270{^\circ}}},}} & \; \\{{{{pdisp}(\theta)} = {{- \left\lbrack {\left\lbrack \frac{stroke}{2} \right\rbrack^{2}\left\lbrack {1 - {\sin^{2}({rad})}} \right\rbrack} \right\rbrack^{1/2}} + \left\lbrack {{conrod}^{2} - {{\sin^{2}({rad})}\left\lbrack \frac{stroke}{2} \right\rbrack}^{2}} \right\rbrack^{1/2}}}{{{{For}\mspace{14mu} 270{^\circ}} \leq \theta < {90{^\circ}}},}} & (2) \\{{{pdisp}(\theta)} = {\left\lbrack {\left\lbrack \frac{stroke}{2} \right\rbrack^{2}\left\lbrack {1 - {\sin^{2}({rad})}} \right\rbrack} \right\rbrack^{1/2} + \left\lbrack {{conrod}^{2} - {{\sin^{2}({rad})}\left\lbrack \frac{stroke}{2} \right\rbrack}^{2}} \right\rbrack^{1/2}}} & (3)\end{matrix}$where pdisp(θ) is the current piston displacement typically expressed inunits of meters (m), stroke is the length of piston travel in cylindertypically expressed in meters (m), rad is the angle of crankshaftrotation θ expressed in radian units (rads), conrod is the length ofconnecting rod typically expressed in meters (m), and sin is thetrigonometric sine.

In the step 815, the volume of gas contained in the head end (V_(HE)) ofthe cylinder may now be determined using, as necessary, knowledge of theclearance percentage for both ends obtained in step 805. As an example,the volume at the head end of the cylinder, V_(HE), may be expressed inthe form of Equation 4.

$\begin{matrix}{V_{HE} = {{\left\lbrack \frac{\pi}{4} \right\rbrack\left\lbrack {{bore}^{2} - \lbrack{tailrod}\rbrack^{2}} \right\rbrack}\left\lbrack {{\left\lbrack \frac{\%\mspace{14mu}{CLR}_{HE}}{100} \right\rbrack*{stroke}} - {{pdisp}(\theta)}} \right\rbrack}} & (4)\end{matrix}$where bore is the piston diameter or the cylinder bore diametertypically expressed in meters (m), tailrod is a tail rod diameter thatis attached to an end of the piston typically expressed in meters (m),and % CLR_(HE) is the cylinder clearance at the head end expressed inpercentage (%).

In Step 820, the crankshaft angle θ is checked as to whether it is lessthan 180 degrees. Since there are two possibilities, each one of themleading to different strokes, firstly the case when θ is less than 180degrees is considered.

Step 840 may involve a calculation of the pressure at the head end ofthe cylinder. As the example, the pressure P_(DA,HE) may be expressed inthe form of Equation 5.

$\begin{matrix}{P_{{DA},{HE}} = {\left\lbrack {{Pd} + {P\; a}} \right\rbrack*\left\lbrack \frac{\%\mspace{14mu}{CLR}_{HE}}{{\%\mspace{14mu}{CLR}_{HE}} - {\frac{{pdisp}(\theta)}{stroke}*100}} \right\rbrack^{kavg}}} & (5)\end{matrix}$

where Pd+Pa is the absolute discharge pressure expressed in kilopascals(kPa), including atmospheric pressure, and kavg is an average ratio ofspecific heats between suction and discharge conditions.

Equation 5 shows the expansion at the head end of the cylinder by way ofpressure increasing with crankshaft angle. At some point during thestroke, the expanding gas in the head end of the cylinder will reach thepressure of the gas in the suction line. Once this occurs, and the valvelosses are overcome, the head end suction valve will open. The crankangle at which this takes place may be found by comparing the pressurein the cylinder to the suction line pressure at the corresponding pistondisplacement of every degree of rotation.

Step 845 shows a comparison of the pressure at head end of the cylinderwith the suction line pressure, Ps+Pa. If the cylinder pressure is notless than or equal to the suction line pressure, the expansion keepscontinuing until the cylinder pressure becomes less than or equal to thesuction line pressure. The pressure is updated for the next incrementalangle until the condition is satisfied. This is shown in Step 847.

If the cylinder pressure equals or is less than the suction linepressure, a linear interpolation is performed to find a more accuratecrank angle for the suction valve opening, i.e., the angle at which thesuction valve opens. This is shown in Step 850. As an example, the crankangle at which the suction valve is open is expressed in the form ofEquation 6. Here the angle of increment is 1 degree and is used as anexample to derive Equation 6. As discussed above, the angle of incrementmay be changed by a user or be set to any value, and as such, is notconsidered limiting.

$\begin{matrix}{{{sv\_ open}{\_\theta}_{HE}} = {\frac{\left\lbrack {{Ps} + {P\; a} - {P_{HE}\left( {{sv\_ open}_{HE} - 1} \right)}} \right\rbrack}{\left\lbrack {{P_{HE}\left( {sv\_ open}_{HE} \right)} - {P_{HE}\left( {{sv\_ open}_{HE} - 1} \right)}} \right\rbrack} + \theta - 1}} & (6)\end{matrix}$where sv_open_θ_(HE) is the crankshaft angle at which the suction valveopens.

As an example, the corresponding volume at the head end may becalculated too in the form of Equation 7.

$\begin{matrix}{{{sv\_ open}{\_ V}_{HE}} = {{\frac{\left\lbrack {{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}} \right\rbrack}{1}*\left\lbrack {{{sv\_ open}{\_\theta}_{HE}} - \left\lbrack {\theta - 1} \right\rbrack} \right\rbrack} + {V_{HE}\left( {\theta - 1} \right)}}} & (7)\end{matrix}$where sv_open_V_(HE) is the volume corresponding to the angle at whichthe suction valve opens.

As an example, the head end suction valve pressure drop may now becalculated in the form of Equation 8

$\begin{matrix}{{\Delta\; P_{{sv},{HE}}} = {{\rho_{sv}\left\lbrack \frac{v^{2}}{2} \right\rbrack}\frac{\left\lbrack {\frac{\pi}{4}\left( {{bore}^{2} - {tailrod}^{2}} \right)} \right\rbrack^{2}}{C_{sv}^{2}*1000}}} & (8)\end{matrix}$where ΔP_(sv,HE) is the head suction value pressure drop expressedtypically in kPa, ρ_(sv) is the density of the gas calculated at suctionconditions expressed typically in kg/m³, and C_(sv) is the suction valvecoefficient expressed typically in m².

The suction and discharge valve coefficients used in calculating thepressure drop across the valves are based on the effective flow area(EFA) of the valve. The EFA is defined as the flow area through anequivalent orifice plate. This value is generally related to the size ofthe cylinder, but may vary according to the valve manufacturer. The RCSuses standardized valve coefficients based on cylinder bore, but thesevalues may require adjustment if the valves have been modified. As thebore gets larger, the cylinder will contain more valves and each valvewill become larger (i.e. increased EFA). The Total EFA per corner is theproduct of the number of valves per corner of the cylinder and the EFAof each valve, as in Equation 9. This is the total flow into (or out of)one end of the cylinder.Total EFA/corner=(No. valves/corner)*(EFA/valve)  (9)

Additionally, in step 850, the difference between the head end pressureand the absolute suction pressure may be accounted for by valve losses.The cylinder pressure may be expressed in the form of Equation 10 as anexample.P _(DA,HE) =Ps+Pa−ΔP _(sv,HE)  (10)

In Step 820, if the crank angle is greater than 180 degrees, i.e., thesecond half of the complete 360 degrees rotation of the crank shaft, thehead end begins the compression stroke. As shown in FIG. 7, in step 852any HydroCOMs present on that end of the cylinder may be checked for asper instruction (1). Only when the HydroCOM is no longer acting on thevalve does the head end suction valve close. Thus, once the condition in(1) is true, the pressure at the head end may be updated for the nextincremented angle until the condition becomes false, as shown in Step854. If the condition becomes false, a precise value for the crank angleat which the HydroCOM stops acting may be found using linearinterpolation as shown in Step 856. Expressed as an example Equation 11,with a 1 degree angle of increment,

$\begin{matrix}{{sv\_ close}_{HE} = {{\frac{1}{{{pdisp}(\theta)} - {{pdisp}\left( {\theta - 1} \right)}}\left\lbrack {{hcom\_ open} - {{pdisp}\left( {\theta - 1} \right)}} \right\rbrack} + \theta - 1}} & (11)\end{matrix}$

The corresponding volume of gas in the head end when the suction valvecloses may also interpolated as example Equation 12,

$\begin{matrix}{{V_{HE}{\_ hcom}} = {{\frac{\left\lbrack {{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}} \right\rbrack}{1}*\left\lbrack {{sv\_ close}_{HE} - \left\lbrack {\theta - 1} \right\rbrack} \right\rbrack} + {V_{HE}\left( {\theta - 1} \right)}}} & (12)\end{matrix}$

The head end cylinder pressure may be calculated in Step 756 as exampleEquation 13,

$\begin{matrix}{P_{{DA},{HE}} = {\left\lbrack {{Ps} + {Pa}} \right\rbrack*\left\lbrack \frac{100 + {\%\mspace{14mu}{CLR}_{HE}}}{{\%\mspace{14mu}{CLR}_{HE}} - {\frac{{pdisp}(\theta)}{stroke}*100}} \right\rbrack^{kavg}}} & (13)\end{matrix}$where Ps+Pa is the absolute suction pressure expressed in kilopascals(kPa).

As the gas trapped in the head end of the cylinder is compressed, thepressure and temperature rise until the pressure in the cylinder exceedsthe pressure in the discharge line by enough to unseat the head enddischarge valve. The point in the compression cycle at which this occursmay be found by comparing the head end cylinder pressure to the knowndischarge line pressure.

In step 858, a comparison may be performed. Specifically, if thecylinder pressure is less than discharge line pressure, the gas in thehead end of the cylinder is still undergoing compression and the headend discharge valve is closed. The pressure may be updated forincremented angle until the comparison yields a false result, as shownin Step 860. If a HydroCOM is acting on the head end suction valve, thepressure drop across the valve may be considered.

In this case, the losses across the suction valve may be added onto theabsolute suction pressure to obtain the head end cylinder pressure inthe form of example Equation 14.P _(DA,HE) =Ps+Pa+ΔP _(sv,HE)  (14)Once the HydroCOM is no longer acting, compression of the remainingvolume of gas in the head end will begin.

Once the condition becomes false, the pressure in the cylinder exceedsthe discharge line pressure and the head end discharge valve opens. Thehead end discharge valve pressure drop may be calculated in the form ofexample Equation 15, using the discharge valve coefficient of the givencylinder and the density of the gas calculated at discharge conditionsas shown in Step 862 as

$\begin{matrix}{{\Delta\; P_{{dv},{HE}}} = {{\rho_{dv}\left\lbrack \frac{v^{2}}{2} \right\rbrack}\frac{\left\lbrack {\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)} \right\rbrack^{2}}{C_{dv}^{2}*1000}}} & (15)\end{matrix}$where ρ_(dv) is the density of the gas calculated at dischargeconditions expressed typically in kg/m³, and C_(dv) is the dischargevalve coefficient expressed typically in m².

When there is no HydroCOM acting on the head end suction valve duringthe compression stroke, the gas will be compressed according to exampleEquation 16.

$\begin{matrix}{P_{{DA},{HE}} = \left\lbrack \frac{\left\lbrack {{P_{HE}\left( {\theta - 1} \right)}*{V_{HE}\left( {\theta - 1} \right)}} \right\rbrack}{V_{HE}(\theta)} \right\rbrack^{kavg}} & (16)\end{matrix}$

If the head end pressure is greater than the absolute dischargepressure, the difference must be accounted for by the valve losses. Inthis case P_(DA,HE) may be redefined as example Equation 17 in Step 862.P _(DA,HE) =Pd+Pa+ΔP _(dv,HE)  (17)FIGS. 9A and 9B:

FIGS. 9A and 9B show the steps involved in calculating the P-V cycle bythe RCS for the compression performed in the head end of the cylinderduring one crankshaft rotation cycle, with the effects of the HydroCOMconsidered. Again, it is obvious to one skilled in the art to see thatthe calculations may be performed without considering the HydroCOMeffects, and as such, the invention should not be limited to consideringthe HydroCOM effects. The calculations for the head end and crank endcompression cycles may also be conducted simultaneously.

In Step 905 the mechanical parameters, and other pre-stored parameterssuch as properties of the gas parameters are obtained. In Step 910, acounter for incrementing crankshaft rotational angle is started from 0to 360 degrees, where the angle of increment may be chosen by a user. Inone or more embodiments of the invention, the piston displacement isdetermined as shown in Step 915, similar to Step 815 of FIG. 7.

In the same Step 915, the volume of gas contained in the crank end ofthe cylinder, V_(CE), may be expressed as Equation 18 as an example.

$\begin{matrix}{V_{CE} = {{{\left\lbrack \frac{\pi}{4} \right\rbrack\left\lbrack {{bore}^{2} - {rod}^{2}} \right\rbrack}\lbrack{stroke}\rbrack}\left\lbrack {1 + \left\lbrack \frac{\%\mspace{14mu}{CLR}_{CE}}{100} \right\rbrack + \left\lbrack \frac{{pdisp}(\theta)}{stroke} \right\rbrack} \right\rbrack}} & (18)\end{matrix}$where rod is the piston rod diameter typically expressed in meters (m).

In Step 920, the crankshaft angle θ is checked to determine whether itis less than 180 degrees. Since there are two possibilities, each one ofthem leads to different strokes.

As the crank end is just beginning the compression stroke, any HydroCOMspresent on that end of the cylinder may be acting. This condition may betested first, as in Instruction (1), and Step 925. Only when it has beendetermined that the HydroCOM is no longer acting on the stroke will thecrank end suction valve close. When a HydroCOM is acting, the pistondisplacement may be updated for incremented angles until the HydroCOMstops acting. This is shown in Step 930.

If the HydroCOM stops acting, a simple linear interpolation may beperformed to find the exact crank angle at which the HydroCOM stopsacting as shown in Step 935, and example Equation 19.

$\begin{matrix}{{{sv\_ close}{\_\theta}_{CE}} = {{\frac{1}{{{pdisp}(\theta)} - {{pdisp}\left( {\theta - 1} \right)}}\left\lbrack {{hcom\_ open} - {{pdisp}\left( {\theta - 1} \right)}} \right\rbrack} + \theta - 1}} & (19)\end{matrix}$where sv_close_θ_(CE) is the angle at which the HydroCOM stops acting,and hcom_open is the point of HydroCOM opening, which may in turn beexpressed as example Equation 20 as:hcom_open=stroke*(1−hcom_pos)  (20)where hcom_pos is the fraction of stroke when HydroCOM is acting.

An interpolation to determine the corresponding cylinder volume may alsobe performed during Step 935. For the closing of the crank end suctionvalve, the volume of gas in the crank end may be interpolation asexample Equation 21:

$\begin{matrix}{{V_{CE}{\_ hcom}} = {{\frac{\left\lbrack {{V_{CE}(\theta)} - {V_{CE}\left( {\theta - 1} \right)}} \right\rbrack}{1}*\left\lbrack {{{sv\_ close}{\_\theta}_{CE}} - \left\lbrack {\theta - 1} \right\rbrack} \right\rbrack} + {V_{CE}\left( {\theta - 1} \right)}}} & (21)\end{matrix}$

The crank end cylinder pressure may be calculated in Step 935 as exampleEquation 22.

$\begin{matrix}{P_{{DA},{CE}} = {\left\lbrack {{Ps} + {Pa}} \right\rbrack*\left\lbrack \frac{100 + {\%\mspace{14mu}{CLR}_{CE}}}{100 + {\%\mspace{14mu}{CLR}_{CE}} + {\frac{{pdisp}(\theta)}{stroke}*100}} \right\rbrack^{kavg}}} & (22)\end{matrix}$where Ps+Pa is the absolute suction pressure expressed in kilopascals(kPa).

During this time, the gas in the crank end of the cylinder is beingcompressed from suction pressure to discharge pressure. As the gas iscompressed, it will reach the pressure of the discharge line, and with asmall amount of differential pressure to overcome the correspondingpressure drop, the gas may open the discharge valve. The point at whichthis occurs may be found by comparing the crank end cylinder pressure tothe known discharge line pressure.

As shown in Step 940, the cylinder pressure is compared with theabsolute suction pressure. If the cylinder pressure is less than theabsolute suction pressure, the crank end discharge valve is closed. Asshown in Step 945, the pressure is updated for incremented angles untilthe cylinder pressure becomes more than the absolute suction pressure.Once this occurs, the pressure in the crank end of the cylinder exceedsthe discharge line pressure and the valve opens. The crank end dischargevalve pressure drop may now be calculated as shown in Step 950 in theform of example Equation 23, using the discharge valve coefficient ofthe given cylinder and the density of the gas calculated at dischargeconditions as,

$\begin{matrix}{{\Delta\; P_{{dv},{CE}}} = {{\rho_{dv}\left\lbrack \frac{v^{2}}{2} \right\rbrack}\frac{\left\lbrack {\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)} \right\rbrack^{2}}{C_{dv}^{2}*1000}}} & (23)\end{matrix}$

If the compressor is equipped with a HydroCOM during the compressionstroke, it may still be acting on the crank end suction valve. If thereis a HydroCOM present, the pressure drop across the crank end suctionvalve must now be considered while the valve remains open during part ofthe compression stroke. The pressure drop may be expressed as exampleEquation 24.

$\begin{matrix}{{\Delta\; P_{{sv},{CE}}} = {{\rho_{sv}\left( \frac{v^{2}}{2} \right)}\frac{\left\lbrack {\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)} \right\rbrack^{2}}{C_{sv}^{2}*1000}}} & (24)\end{matrix}$

As the gas is now flowing out of the cylinder through the suction valve,the losses across the suction valve may be added to the suction pressureto find the cylinder pressure until the HydroCOM is no longer acting onthe valve. The pressure may be expressed as example Equation 25.P _(DA,CE) =Ps+Pa+ΔP _(sv,CE)  (25)

If the compressor is not equipped with a HydroCOM, it is only requiredto calculate the pressure. At θ=0, the crank end of the cylinder isknown to be at maximum volume since the piston is at top dead center(TDC). Thus, at this point, the crank end pressure may be expressed asexample Equation 26.P _(DA,CE) =Ps+Pa(for θ=0)  (26)

Otherwise, the pressure may be expressed in Step 850 as example Equation27.

$\begin{matrix}{{P_{{DA},{CE}} = \left\lbrack \frac{\left\lbrack {{P_{CE}\left( {\theta - 1} \right)}*{V_{CE}\left( {\theta - 1} \right)}} \right\rbrack}{V_{CE}(\theta)} \right\rbrack^{kavg}}\left( {{{for}\mspace{14mu} 0} < \theta<=180} \right)} & (27)\end{matrix}$If the crank end pressure is greater than the absolute dischargepressure, the difference must be accounted for by the valve losses. Inthis case P_(DA,CE) may be redefined as example Equation 28:P _(DA,CE) =Pd+Pa+ΔP _(dv,CE)  (28)

In Step 920, if the crank angle is greater than 180 degrees, i.e., thesecond half of the complete 360 degrees rotation of the crank shaft, thecrank end begins the expansion stroke. The cylinder pressure may becalculated in Step 955 as example Equation 29.

$\begin{matrix}{P_{{DA},{CE}} = {\left\lbrack {{Pd} + {Pa}} \right\rbrack*\left\lbrack \frac{\%\mspace{14mu}{CLR}_{CE}}{100 + {\%\mspace{14mu}{CLR}_{CE}} + {\frac{{pdisp}(\theta)}{stroke}*100}} \right\rbrack^{kavg}}} & (29)\end{matrix}$

The gas in the crank end expands back to suction pressure. The crank endsuction valve will open when the cylinder pressure is less than or equalto the absolute suction pressure. This condition may be tested for inStep 960. If false, the pressure is updated for incremented angles untilthe condition becomes true as shown in Step 965. When true, the crankangle at which the cylinder pressure equals absolute suction pressuremay be obtained in Step 970 by a simple linear interpolation as shown inexample Equation 30.

$\begin{matrix}{{{sv\_ open}{\_\theta}_{CE}} = {\frac{{Ps} + {Pa} - {P_{CE}\left( {{sv\_ open}_{CE} - 1} \right)}}{{P_{CE}\left( {sv\_ open}_{CE} \right)} - {P_{CE}\left( {{sv\_ open}_{CE} - 1} \right)}} + \theta - 1}} & (30)\end{matrix}$

The corresponding volume may also be obtained by another interpolationas shown in example Equation 31 with a 1 degree angle of increment.

$\begin{matrix}{{{sv\_ open}{\_ V}_{CE}} = {{\frac{{V_{CE}(\theta)} - {V_{CE}\left( {\theta - 1} \right)}}{1}*\left\lbrack {{{sv\_ open}{\_\theta}_{CE}} - \left( {\theta - 1} \right)} \right\rbrack} + {V_{CE}\left( {\theta - 1} \right)}}} & (31)\end{matrix}$

The crank end suction valve pressure drop may be determined from exampleEquation 32 using the suction valve coefficient and the density of thegas calculated at suction conditions.

$\begin{matrix}{{\Delta\; P_{{sv},{CE}}} = {{\rho_{sv}\left\lbrack \frac{v^{2}}{2} \right\rbrack}\frac{\left\lbrack {\frac{\pi}{4}\left( {{bore}^{2} - {tailrod}^{2}} \right)} \right\rbrack^{2}}{C_{sv}^{2}*1000}}} & (32)\end{matrix}$If the crank end cylinder pressure is less than absolute suctionpressure, the difference may be accounted for by the losses across thesuction valve. The cylinder pressure may be expressed as exampleEquation 33 as,P _(DA,CE) =Ps+Pa−ΔP _(sv,CE)  (33)

Equations 4 through 33 define the points on the P-V diagram for eachangle of rotation of the crankshaft. In one or more embodiments of theinvention, the data may thus be used not only for creating an accuraterepresentation of the P-V diagram, but also as the basis for conductinga road load analysis using the RCS. Before discussing the rod loadanalysis, calculating power losses and temperature rise across valves isdiscussed below.

In one or more embodiments of the invention, the RCS may also calculatepower losses imposed by the suction and discharge valve from thepressure drop across each valve discussed above.

When the angle is between 0 and 180 degrees, the power losses may becalculated for successive angles in the form of example Equations 34 and35.

$\begin{matrix}{{\overset{.}{W}}_{{loss}{({{sv},{HE}})}} = {{\overset{.}{W}}_{{loss}{({{sv},{HE}})}} + {\left\lbrack \mspace{20mu}\frac{{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}}{60} \right\rbrack*N*\Delta\; P_{{sv},{HE}}}}} & (34) \\{{\overset{.}{W}}_{{loss}{({{dv},{CE}})}} = {{\overset{.}{W}}_{{loss}{({{dv},{CE}})}} + {{\frac{{V_{CE}(\theta)} - {V_{CE}\left( {\theta - 1} \right)}}{60}}*N*\Delta\; P_{{dv},{CE}}}}} & (35)\end{matrix}$where N is the crankshaft rotational speed expressed typically inrevolutions per minute (rpm).

In one or more embodiments of the invention, the effects of a HydroCOMmay be considered in the power loss due to the recycle through the crankend suction valve as example Equation 36.

$\begin{matrix}{{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}{\_ hcom}} = {{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}{\_ hcom}} + {{\frac{{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}}{60}}*N*\Delta\; P_{{sv},{CE}}}}} & (36)\end{matrix}$

When the angle is between 180 and 360 degrees, the power losses may beexpressed in the form of example Equations 37 and 38.

$\begin{matrix}{{\overset{.}{W}}_{{loss}{({{dv},{HE}})}} = {{\overset{.}{W}}_{{loss}{({{dv},{HE}})}} + {\left\lbrack \frac{{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}}{60} \right\rbrack*N*\Delta\; P_{{dv},{HE}}}}} & (37) \\{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}} = {{\overset{.}{W}}_{{loss}{({{sv},{CE}})}} + {{\frac{{V_{CE}(\theta)} - {V_{CE}\left( {\theta - 1} \right)}}{60}}*N*\Delta\; P_{{sv},{CE}}}}} & (38)\end{matrix}$

In one or more embodiments of the invention, the effects of a HydroCOMmay be considered in the power loss due to the recycle through the headend suction valve as example Equation 39.

$\begin{matrix}{{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}{\_ hcom}} = {{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}{\_ hcom}} + {{\frac{{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}}{60}}*N*\Delta\; P_{{sv},{CE}}}}} & (39)\end{matrix}$

In one or more embodiments of the invention, in order to calculate thetemperature rise across each set of valves, the mass flow rate of gasthrough each end of the cylinder may be calculated according to exampleEquations 40-43. It is to be noted that all flows may be calculated withrespect to the suction end of the P-V diagram.

$\begin{matrix}{{\overset{.}{m}}_{HE} = \frac{{{{{sv\_ open}{\_ V}_{HE}} - {V_{HE}\left( {180{^\circ}} \right)}}}*N*\rho_{s}}{60}} & (40) \\{{\overset{.}{m}}_{CE} = \frac{{{{{sv\_ open}{\_ V}_{CE}} - {V_{CE}\left( {0{^\circ}} \right)}}}*N*\rho_{s}}{60}} & (41) \\{{{\overset{.}{m}}_{HE}{\_ hcom}} = \frac{{{{{sv\_ open}{\_ V}_{HE}} - {V_{HE}\left( {180{^\circ}} \right)}}}*N*\rho_{s}}{60}} & (42) \\{{{\overset{.}{m}}_{CE}{\_ hcom}} = \frac{{{{{sv\_ open}{\_ V}_{CE}} - {V_{CE}\left( {0{^\circ}} \right)}}}*N*\rho_{s}}{60}} & (43)\end{matrix}$

In one or more embodiments of the invention, for each end of thecylinder that has a positive mass flow rate, the temperature rise may becalculated across the suction valves, acting HydroCOMs, and dischargevalves using the form of example Equations 44-49.

$\begin{matrix}{{\Delta\; T_{{sv},{HE}}} = \frac{{\overset{.}{W}}_{{loss}{({{sv},{HE}})}}}{\left( c_{p,s} \right)\left( {\overset{.}{m}}_{HE} \right)}} & (44) \\{{\Delta\; T_{{sv},{HE}}{\_ hcom}} = \frac{{\overset{.}{W}}_{{loss}{({{sv},{HE}})}}{\_ hcom}}{\left( c_{p,s} \right)\left( {{\overset{.}{m}}_{HE}{\_ hcom}} \right)}} & (45) \\{{\Delta\; T_{{dv},{HE}}} = \frac{{\overset{.}{W}}_{{loss}{({{dv},{HE}})}}}{\left( c_{p,d} \right)\left( {\overset{.}{m}}_{HE} \right)}} & (46) \\{{\Delta\; T_{{sv},{CE}}} = \frac{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}}{\left( c_{p,s} \right)\left( {\overset{.}{m}}_{CE} \right)}} & (47) \\{{\Delta\; T_{{sv},{CE}}{\_ hcom}} = \frac{{\overset{.}{W}}_{{loss}{({{sv},{CE}})}}{\_ hcom}}{\left( c_{p,s} \right)\left( {{\overset{.}{m}}_{CE}{\_ hcom}} \right)}} & (48) \\{{\Delta\; T_{{dv},{CE}}} = \frac{{\overset{.}{W}}_{{loss}{({{dv},{CE}})}}}{\left( c_{p,d} \right)\left( {\overset{.}{m}}_{CE} \right)}} & (49)\end{matrix}$Here the subscripts s and d refer to suction and discharge valves. c_(p)and c_(v) refer to the specific heat of gas at constant pressure andvolume respectively, and are typically expressed in kJ/kg·K.

In one or more embodiments of the invention, if HydroCOMs are actingthen the temperature rise caused by flow back through the valve may beadded to the suction valve temperature rise for each end as shown inexample Equations 50 and 51.ΔT _(sv,HE) =ΔT _(sv,HE) +ΔT _(sv,HE—) hcom  (50)ΔT _(sv,HE) =ΔT _(sv,HE) +ΔT _(sv,HE—) hcom  (51)

In one or more embodiments of the inventions, the Performance Report ofthe compressor system may involve calculations of average temperaturerises through valves. These may be obtained by summing the temperaturerise across each set of valves in one stage and dividing by the numberof acting cylinder ends (e.g., DA=2, SA=1) in the same stage. The samecalculation method applies on a per cylinder basis. Equations 52-55 areshown as example average temperature rises.

$\begin{matrix}{{\Delta\; T_{{sv},\;{cyl}}} = \frac{{\Delta\; T_{{sv},\;{HE}}} + {\Delta\; T_{{sv},\;{CE}}}}{\beta}} & (52) \\{{\Delta\; T_{{dv},\;{cyl}}} = \frac{{\Delta\; T_{{dv},\;{HE}}} + {\Delta\; T_{{dv},\;{CE}}}}{\beta}} & (53) \\{{\Delta\; T_{{sv},\;{stg}}} = \frac{\sum\limits_{stg}{\Delta\; T_{{sv},\;{cyl}}}}{\sum\limits_{stg}\beta}} & (54) \\{{\Delta\; T_{{dv},\;{stg}}} = \frac{\sum\limits_{stg}{\Delta\; T_{{dv},\;{cyl}}}}{\sum\limits_{stg}\beta}} & (55)\end{matrix}$The subscripts “stg” refers to stage, and cyl refers to cylinder. Here βrefers to the number of acting ends in the cylinder.

In one or more embodiments of the invention, the total power lossesacross the suction and discharge valves for each stage may be given bythe sum of the losses from each end of each cylinder. Equations 56-57are shown as an example.

$\begin{matrix}{{\overset{.}{W}}_{{loss},\;{{sv}{({stg})}}} = {\sum\limits_{stg}\left( {{\overset{.}{W}}_{{loss}{({{sv},\;{HE}})}} + {\overset{.}{W}}_{{loss}{({{sv},\;{CE}})}}} \right)}} & (56) \\{{\overset{.}{W}}_{{loss},\;{{dv}{({stg})}}} = {\sum\limits_{stg}\left( {{\overset{.}{W}}_{{loss}{({{dv},\;{HE}})}} + {\overset{.}{W}}_{{loss}{({{dv},\;{CE}})}}} \right)}} & (57)\end{matrix}$

In one or more embodiments of the invention, the P-V calculations mayalso serve as a basis to calculate the theoretical power consumed by acompressor, which may be defined as the area enclosed within its P-Vdiagram. As discussed above, to obtain accurate power predictions, theReciprocating Compressor Simulator performs a numerical integration ofthe P-V diagram generated in the previous section. This integration mayperformed using the trapezoidal rule, which is one of the Newton-Cotesclosed integration formulas. The general formula for integrating the P-Vdiagram using this method may be expressed by example Equations 58 and59 as

$\begin{matrix}{{\overset{.}{W}}_{HE} = {{\frac{{V_{HE}(\theta)} - {V_{HE}\left( {\theta - 1} \right)}}{60}}*N*\left\lbrack \frac{{P_{HE}\left( \theta^{\prime} \right)} - {P_{HE}(\theta)} + {P_{HE}\left( {\theta^{\prime} + 1} \right)} - {P_{HE}\left( {\theta - 1} \right)}}{2} \right\rbrack}} & (58) \\{{\overset{.}{W}}_{CE} = {{\frac{{V_{CE}(\theta)} - {V_{CE}\left( {\theta - 1} \right)}}{60}}*N*\left\lbrack \frac{{P_{CE}\left( \theta^{\prime} \right)} - {P_{CE}(\theta)} + {P_{CE}\left( {\theta^{\prime} + 1} \right)} - {P_{CE}\left( {\theta - 1} \right)}}{2} \right\rbrack}} & (59)\end{matrix}$Here θ and θ′ are the lower and upper angle limits of integration, andthe incremental angle shown as 1 for example purposes.

Thus, in one or more embodiments of the invention, with substitution ofappropriate variables, the head end and crank end P-V diagrams of eachcylinder may be integrated separately and then added together to givethe total power consumption of each cylinder, each stage, and the entirecompressor. Supplemental equations may be expressed as example Equations60-62.

Average power consumed may be expressed as

$\begin{matrix}{{\overset{.}{W}}_{cyl} = \frac{{\overset{.}{W}}_{HE} + {\overset{.}{W}}_{CE}}{\eta_{mech}}} & (60)\end{matrix}$Here η_(mech) is the mechanical efficiency of the compressor.

$\begin{matrix}{{\overset{.}{W}}_{stg} = {\sum\limits_{{stg}\;}^{\;}\;{\overset{.}{W}}_{cyl}}} & (61) \\{{\overset{.}{W}}_{overall} = {\sum\limits_{\;}^{\;}\;{\overset{.}{W}}_{cyl}}} & (62)\end{matrix}$

In one or more embodiments of the invention, the theoretical flowthrough each stage of the compressor may be calculated. Since thecylinder volumes where the suction valve opens and closes preciselydefine the suction portion of the P-V diagram, it is possible todetermine the flow based on the suction valve action and the gasproperties at suction conditions. It is to be noted that by the sametheory, it is also possible to determine the flow based on the dischargeportion of the P-V diagram.

If the compressor has acting HydroCOMs, a calculation may be performedto determine the amount of flow is lost through the cylinder due to theHydroCOM recycling the flow back to the suction line. Equations of flowloss due to HydroCOM 63 and 64 are shown as examples.

$\begin{matrix}{{Q_{{std},{HE}}{\_ hcom}} = {\left\lbrack {\frac{{V_{HE}\left( {180{^\circ}} \right)} - {V_{HE}{\_ hcom}}}{{{\left\lbrack {273.15 + {Ts} + {\Delta\; T_{{sv},{HE}}}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}} \right\rbrack*N*60}} & (63) \\{{Q_{{std},{CE}}{\_ hcom}} = {\left\lbrack {\frac{{V_{CE}\left( {0{^\circ}} \right)} - {V_{CE}{\_ hcom}}}{{{\left\lbrack {273.15 + {Ts} + {\Delta\; T_{{sv},{CE}}}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}} \right\rbrack*N*60}} & (64)\end{matrix}$The flow is typically expressed in cubic meters/hour (m³/h). Zs is thesuction valve resistance.

In one or more embodiments of the invention, when the flows arecalculated based on the suction portion of the P-V diagram, thetemperature rise across the valve is accounted for by breaking theequation into two terms as shown above. The temperature rise is addedinto the first term, at the point where the suction valve normallycloses (maximum cylinder volume), but not into the second term as notemperature rise has occurred at that point. This method represents alinear approximation of the temperature rise across the valve as gas isflowing through.

Actual flow through cylinder may be expressed as example Equations 65and 66.

$\begin{matrix}{Q_{{std},{HE}} = {\left\lbrack {{\frac{V_{HE}\left( {180{^\circ}} \right)}{{{\left\lbrack {273.15 + {Ts} + {\Delta\; T_{{sv},{HE}}}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}} - {\frac{{sv\_ open}{\_ V}_{HE}}{{{\left\lbrack {273.15 + {Ts}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}}} \right\rbrack*N*60}} & (65) \\{Q_{{std},{CE}} = {\left\lbrack {{\frac{V_{CE}\left( {0{^\circ}} \right)}{{{\left\lbrack {273.15 + {Ts} + {\Delta\; T_{{sv},{CE}}}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}} - {\frac{{sv\_ open}{\_ V}_{CE}}{{{\left\lbrack {273.15 + {Ts}} \right\rbrack\left\lbrack \frac{288.15}{101.325} \right\rbrack}\left\lbrack {{Ps} + {P\; a}} \right\rbrack}\lbrack{Zs}\rbrack}*\frac{24}{1000}}} \right\rbrack*N*60}} & (66)\end{matrix}$

The theoretical flow through each stage of the compressor may then beexpressed as the sum of the flows through each cylinder in the stage,accounting for any HydroCOM recycle, as shown in example Equation 67.

$\begin{matrix}{Q_{{std},{stg}} = {\sum\limits_{cyl}^{\;}\;\left( {Q_{{std},{HE}} + Q_{{std},{CE}} - {Q_{{std},{HE}}{\_ hcom}} - {Q_{{std},{CE}}{\_ hcom}}} \right)}} & (67)\end{matrix}$

In one or more embodiments of the invention, the volumetric efficiencyof each cylinder may also be calculated by the RCS using the volumescalculated for the opening and closing of valves on the generated P-Vdiagram. The exact crank angles for opening of the suction valves may beused. The volumetric efficiency may be expressed as example Equations 68and 69.

$\begin{matrix}{\eta_{v,{HE}} = \frac{{V_{HE}\left( {180{^\circ}} \right)} - {{sv\_ open}{\_ V}_{HE}}}{{V_{HE}\left( {180{^\circ}} \right)} - {V_{HE}\left( {0{^\circ}} \right)}}} & (68) \\{\eta_{v,{CE}} = \frac{{V_{CE}\left( {0{^\circ}} \right)} - {{sv\_ open}{\_ V}_{CE}}}{{V_{CE}\left( {0{^\circ}} \right)} - {V_{CE}\left( {180{^\circ}} \right)}}} & (69)\end{matrix}$

The theoretical discharge temperature of the gas in each cylinder isbased on the first principle thermodynamic equation for temperatureincrease of a compressed gas. At the moment the discharge valve opens,the temperature in the cylinder may be given by example Equation (70) as

$\begin{matrix}{{Td}_{valve} = {{\left\lbrack {{Ts} + 273.15 + {\Delta\; T_{{sv},{cyl}}}} \right\rbrack\left\lbrack \frac{{Pd} + {P\; a}}{{Ps} + {P\; a}} \right\rbrack}^{\frac{{kavg} - 1}{kavg}} - 273.15}} & (70)\end{matrix}$Note that here temperature is in Kelvins (K).

The RCS may account for the temperature rise through both the suctionand discharge valves, as discussed above. Thus, for each cylinder, thetheoretical discharge temperature may be calculated as example Equation(71) in accordance with one or more embodiments of the invention.

$\begin{matrix}{{Td}_{valve} = {{\left\lbrack {{Ts} + 273.15 + {\Delta\; T_{{sv},{cyl}}}} \right\rbrack\left\lbrack \frac{{P\; d} + {P\; a}}{{Ps} + {P\; a}} \right\rbrack}^{\frac{{kavg} - 1}{kavg}} - 273.15 + {\Delta\; T_{{dv},{cyl}}}}} & (71)\end{matrix}$

The theoretical discharge temperature of each stage may then beexpressed as the average of the discharge temperature of each cylinder.

$\begin{matrix}{{Td} = \frac{\sum\limits_{stg}{Td}_{cyl}}{\sum\limits_{stg}{cyl}}} & (72)\end{matrix}$

As discussed above, the RCS may also be capable of calculating the totalloads on the piston rods of a compressor given the weight of thereciprocating assembly and the information determined while creating theP-V diagram. The RCS may also be expanded to include the calculation ofthe loads on the connecting rod and connecting rod bolts.

In one or more embodiments of the invention, the angle of the connectingrod is a function of the angle of rotation of the crankshaft and isgiven by example Equation 73:

$\begin{matrix}{\phi = {\arctan\left\lbrack \frac{\frac{{\sin({rad})}*{stroke}}{2*{conrod}}}{\left\lbrack {{- {\left\lbrack \frac{{\sin({rad})}*{stroke}}{2*{conrod}} \right\rbrack\left\lbrack \frac{{\sin({rad})}*{stroke}}{2*{conrod}} \right\rbrack}} + 1} \right\rbrack^{1/2}} \right\rbrack}} & (73)\end{matrix}$

In one or more embodiments of the invention, the equations for velocityand acceleration of the reciprocating assembly defined at the crosshead,and the angular velocity and angular acceleration of the connecting rodmay be derived by kinematics and expressed as example Equations 74-77.

Angular Velocity of Connecting Rod:

$\begin{matrix}{\omega = {{\left\lbrack \frac{2\pi\; N}{60} \right\rbrack\left\lbrack \frac{stroke}{2} \right\rbrack}\left\lbrack \frac{\cos({rad})}{{\cos(\phi)}*{conrod}} \right\rbrack}} & (74)\end{matrix}$Velocity at Crosshead:

$\begin{matrix}{v = {{{\left\lbrack \frac{2\pi\; N}{60} \right\rbrack\left\lbrack \frac{stroke}{2} \right\rbrack}{\sin({rad})}} + {\omega*{conrod}*{\sin(\phi)}}}} & (75)\end{matrix}$Angular Acceleration of Connecting Rod:

$\begin{matrix}{\alpha = {{{\left\lbrack \frac{2\pi\; N}{60} \right\rbrack^{2}\left\lbrack \frac{stroke}{2} \right\rbrack}\left\lbrack \frac{\sin({rad})}{{\cos(\phi)}*{conrod}} \right\rbrack} - {\omega^{2}{\tan(\phi)}}}} & (76)\end{matrix}$Acceleration at Crosshead:

$\begin{matrix}{a = {{\left\lbrack \frac{2\pi\; N}{60} \right\rbrack^{2}\left\lbrack \frac{stroke}{2} \right\rbrack}\left\lbrack {\frac{{\cos({rad})} + {stroke}}{2*{conrod}}*{\cos\left( {2*{rad}} \right)}} \right\rbrack}} & (77)\end{matrix}$

In one or more embodiments of the invention, the data displayed in theRod Load Report may include the inertia load, pressure load, and totalload. These loads are calculated for each degree of crankshaft rotationfor each cylinder in a compressor.

The inertia load is defined as the load created by the dynamic forcesrequired to accelerate the mass of the piston and rod assembly,otherwise called the reciprocating mass. The reciprocating mass isdefined as the sum of the masses of the following components: piston,piston rod, piston nut, crosshead, crosshead pin, crosshead nut, andbalance mass. The inertia load may then be defined as a function of therotation of the crankshaft and expressed in example Equation 78 as:{right arrow over (F)} _(I)(θ)=m_(recip) *a  (78)Here m_(recip) is the reciprocating mass typically expressed inkilograms (kg).

The pressure load, or internal gas load, is the force on the pistonresulting from the compression of the gas in the cylinder. As the gas iscompressed, the resulting pressure force increases. The pressure loadincludes the static load, which is the load due to the difference inpressure across the piston, calculated at the maximum suction anddischarge pressure in the cylinder. Valve losses are not taken intoaccount for the calculation of static load as the pressure may bemeasured by gauges on the outside of the compressor. This condition willexist when the compressor is pressurized but not operating. The staticload may thus be defined for each cylinder configuration independent ofthe rotation of the crankshaft.

The internal gas load may be mathematically defined similarly to thestatic load, except that the internal gas load accounts for the internalpressure drop due to valve losses and is dependent entirely on thepressure within the cylinder at any given angle of rotation of thecrankshaft. The following example Equations 79-90 present the staticload and internal gas load for all four different cylinderconfigurations.

SAHE (Single Acting Head End):

$\begin{matrix}{{\overset{\rightharpoonup}{F}}_{{static},\;{tension}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (79) \\{{\overset{\rightharpoonup}{F}}_{{static},\;{compression}} = {\left\lbrack {{{- \left( {{Pd} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (80) \\{{{\overset{\rightharpoonup}{F}}_{P}(\theta)} = {\left\lbrack {{{- P_{{DA},\;{HE}}}*\frac{\pi}{4}*{bore}^{2}} + {P_{SA}*\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (81)\end{matrix}$

SACE (Single Acting Crank End):

$\begin{matrix}{{\overset{\rightharpoonup}{F}}_{{static},\;{tension}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Pd} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (82) \\{{\overset{\rightharpoonup}{F}}_{{static},\;{compression}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (83) \\{{{\overset{\rightharpoonup}{F}}_{P}(\theta)} = {\left\lbrack {{{- P_{SA}}*\frac{\pi}{4}*{bore}^{2}} + {P_{{DA},\;{CE}}*\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (84)\end{matrix}$

DA (Double Acting):

$\begin{matrix}{{\overset{\rightharpoonup}{F}}_{{static},\;{tension}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Pd} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (85) \\{{\overset{\rightharpoonup}{F}}_{{static},\;{compression}} = {\left\lbrack {{{- \left( {{Pd} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (86) \\{{{\overset{\rightharpoonup}{F}}_{P}(\theta)} = {\left\lbrack {{{- P_{{DA},\;{HE}}}*\frac{\pi}{4}*{bore}^{2}} + {P_{{DA},\;{CE}}*\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (87)\end{matrix}$

NA (Non-Acting):

$\begin{matrix}{{\overset{\rightharpoonup}{F}}_{{static},\;{tension}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (88) \\{{\overset{\rightharpoonup}{F}}_{{static},\;{compression}} = {\left\lbrack {{{- \left( {{Ps} + {P\; a}} \right)}\frac{\pi}{4}*{bore}^{2}} + {\left( {{Ps} + {P\; a}} \right)\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}} & (89) \\{\mspace{79mu}{{{\overset{\rightharpoonup}{F}}_{p}(\theta)} = {\left\lbrack {{{- P_{SA}}*\frac{\pi}{4}*{bore}^{2}} + {P_{SA}*\frac{\pi}{4}\left( {{bore}^{2} - {rod}^{2}} \right)}} \right\rbrack*1000}}} & (90)\end{matrix}$

The total load on the piston rod may then be expressed the algebraic sumof the inertia load and the internal gas load for every degree ofrotation of the crankshaft as shown in example Equation 91{right arrow over (F)} _(rod)(θ)=Σ({right arrow over (F)} _(I)(θ)+{rightarrow over (F)} _(P)(θ))  (91)FIG. 10:

FIG. 10 shows an example of how the inertia load 1070, pressure load1065 and total load 1075 may be presented as a Rod Load Report. It isobvious to one skilled in the art to see that it is possible tographically determine the total load 1075 given the inertia and pressureload diagrams. The inertia and pressure loads tend to oppose each other,especially near TDC and BDC. This is important for balancing the load onthe piston rod and keeping the total load within the allowable limitsfor tension (1040) and compression (1060) specified by the manufacturer.It is undesirable to run a reciprocating compressor at very highpressures and low speeds or at very high speed with little or nopressure load, as balance is not achieved in those conditions.

As discussed above, reversal of load between tension and compression inthe piston rod is required at the crosshead pin and bushing for adequatelubrication of the joint. In one or more embodiments of the invention,the number of degrees of rod reversal may be calculated by the RCS bychecking the total load at each degree of crankshaft rotation. If theload is positive, a counter for degrees of positive load may beincremented, and likewise a counter for degrees of negative load may beincremented if the total load is negative. The smallest number of thetwo counters is the degrees of reversal. Points of load reversal may belocated at angles where the total rod load is 0.

It is to be noted that the force reversal does not occur at the samecrank angle as the pressure reversal due to different piston surfaceareas between head end and crank end. Also, while the inertia load is areversing load by definition, the internal gas load is not always areversing load, depending on the configuration of the cylinder.

In one or more embodiments of the invention, at the end of thecalculation loop for each degree of crankshaft rotation, each loadingtype may be compared to a variable holding the previous maximum andminimum load. The final values may then be displayed on the Rod LoadReport in addition to the diagrams.

The RCS may also calculate the loads on the connecting rod due to thehorizontal acceleration of the connecting rod. In the same way as thepiston rod load is measured at the crosshead pin, the load on theconnecting rod is measured at the main bushing where the connecting rodjoins to the crankshaft. The acceleration may be expressed as exampleEquation 92

$\begin{matrix}{a_{{horiz},\;{cr}} = {{\left\lbrack \frac{2\pi\; N}{60} \right\rbrack^{2}*\frac{stroke}{2}*{\cos({rad})}} - {\frac{\alpha}{4}*{conrod}*{\sin(\phi)}} + {\frac{\omega^{2}}{4}*{conrod}*{\cos(\phi)}}}} & (92)\end{matrix}$Here φ is the connecting rod angle expressed in radians.

If the weight of the connecting rod has been defined, the load may nowbe determined by summing the product of the connecting rod mass andacceleration for every degree of crankshaft rotation and expressed asexample Equation (93)

$\begin{matrix}{{{\overset{\rightharpoonup}{F}}_{cr}(\theta)} = {\sum\frac{m_{cr}*a_{{horiz},\;{cr}}}{\cos(\phi)}}} & (93)\end{matrix}$Here m_(cr) is the connecting rod mass typically expressed in kg.

Unlike the piston rod, which is one piece and commonly threaded at bothends, the connecting rod may be made of two pieces which are boltedtogether: the rod and the cap. If the bolted joint fails, the piston maybe pushed into the cylinder head and resulting in a catastrophic failurewith loss of containment. In one or more embodiments of the invention,the RCS may include instructions based on the necessary equations foranalyzing the bolted joint.

FIG. 11:

Embodiments of the invention may be implemented on virtually any type ofcomputer regardless of the platform being used. For example, as shown inFIG. 11, a computer system (1100) includes one or more processor(s)(1102), associated memory (1104) (e.g., random access memory (RAM),cache memory, flash memory, etc.), a storage device (1106) (e.g., a harddisk, an optical drive such as a compact disk drive or digital videodisk (DVD) drive, a flash memory stick, etc.), and numerous otherelements and functionalities typical of today's computers (not shown).The computer (1100) may also include input means, such as a keyboard(1108), and a mouse (1110). Further, the computer (400) may includeoutput means, such as a monitor (412) (e.g., a liquid crystal display(LCD), a plasma display, a plotter, or cathode ray tube (CRT) monitor).The computer system (1100) may be connected to a network (1114) (e.g., alocal area network (LAN), a wide area network (WAN) such as theInternet, or any other similar type of network) via a network interfaceconnection (not shown). Those skilled in the art will appreciate thatmany different types of computer systems exist, and the aforementionedinput and output means may take other forms. Generally speaking, thecomputer system (1100) includes at least the minimal processing, input,and/or output means necessary to practice embodiments of the invention.

Illustrative Embodiments:

In one embodiment, there is disclosed a method comprising operatingequipment comprising a piston within a cylinder; obtaining parameters ofthe equipment from a data repository; calculating a P-V cycle as afunction of a crankshaft rotation angle; calculating a rod load usingthe P-V cycle values. In some embodiments, the method also includesusing correctional measures for keeping the rod load below pre-definedlevels.

In one embodiment, there is disclosed a method comprising operating acompressor; obtaining operating parameters of the compressor; starting acounter for a crankshaft angle from 0 to 360 degrees; calculating pistondisplacement and a volume of gas in a cylinder of the compressor as afunction of the angle; and calculating a pressure within the cylinder.In some embodiments, the method also includes determining if thecylinder pressure is greater than a suction line pressure. In someembodiment, the method also includes determining an angle at which asuction valve opened, and determining the suction valve pressure loss.In some embodiments, the method also includes calculating a power losscaused by the suction valve. In some embodiments, the method alsoincludes determining if the cylinder pressure is greater than adischarge line pressure. In some embodiments, the method also includesdetermining a discharge valve pressure loss. In some embodiments, themethod also includes calculating a power loss caused by the dischargevalve. In some embodiments, the method also includes calculating actualand theoretical flow through the cylinder. In some embodiments, themethod also includes calculating total power consumption of thecylinder. In some embodiments, the method also includes calculating aP-V diagram for the cylinder. In some embodiments, the method alsoincludes calculating a temperature change across at least one valve ofthe cylinder.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art, having benefit of thisdisclosure, will appreciate that other embodiments may be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theattached claims.

That which is claimed is:
 1. A method comprising: operating equipmentcomprising a piston within a cylinder; obtain equipment parameters fromthe operating equipment; reporting at least one operating parameter to adata repository; obtaining parameters of the equipment from the datarepository; calculating a P-V cycle as a function of a crankshaftrotation angle; calculating a rod load using the P-V cycle values;determining if the cylinder pressure is greater than a suction linepressure determining an angle at which a suction valve opened; anddetermining the suction valve pressure loss.
 2. The method of claim 1,further comprising using correctional measures for keeping the rod loadbelow pre-defined levels.
 3. A method comprising: operating acompressor; obtaining operating parameters of the compressor; starting acounter for a crankshaft angle from 0 to 360 degrees; calculating pistondisplacement and a volume of gas in a cylinder of the compressor as afunction of the angle; calculating a pressure within the cylinder;determining if the cylinder pressure is greater than a suction linepressure; determining an angle at which a suction valve opened; anddetermining the suction valve pressure loss.
 4. The method of claim 3,further comprising: calculating a power loss caused by the suctionvalve.
 5. The method of claim 3, further comprising: determining if thecylinder pressure is greater than a discharge line pressure.
 6. Themethod of claim 3, further comprising: determining a discharge valvepressure loss.
 7. The method of claim 3, further comprising: calculatinga power loss caused by the discharge valve.
 8. The method of claim 3,further comprising: calculating actual and theoretical flow through thecylinder.
 9. The method of claim 3, further comprising: calculatingtotal power consumption of the cylinder.
 10. The method of one claim 3,further comprising: calculating a P-V diagram for the cylinder.
 11. Themethod of claim 3, further comprising: calculating a temperature changeacross at least one valve of the cylinder.